It is modeled by an artificial neural network with two hidden layers of 10 units each. The (differentiable) exponential linear unit with shape parameter \(a = 1\)  (see [1]}) is used as activation function for all neurons. The inputs of the network are the states \(x_1\)  and \(x_2\) . Note that, if the value of \(A\)  would be uncertain, we could include \(\sin (\omega t)\)  as an extra input to the network (i.e., \(u(t) = \sin (\omega t)\)  in (REF )) to also learn the model error related to an incorrect estimate of \(A\) . The outputs of the network are the functions \(f_{\text{net},1}(\mathbf {x}(t))\)  and \(f_{\text{net},2}(\mathbf {x}(t))\)  that represent the estimates of the two elements of the error vector. Because there exist no network parameters that represent the model error exactly for all values of \(\mathbf {x}\) , the network provides only a local approximation of the model error. The network is trained based on noisy measurements of the (full) state of the system. The measurements are taken from time \(t = 0\)  to time \(t = 100\) , with a step size of \(0.1\)  between subsequent measurements. The measurement noise has a Gaussian distribution with a zero mean and a variance of 0.01.
